Selective excitation localized by the Bloch-Siegert shift and a B1+ gradient

Abstract

Purpose: To perform $B_1^{+}$ -selective excitation using the Bloch-Siegert shift for spatial localization.

Theory and methods: A $B_1^{+}$ -selective excitation is produced by an radiofrequency (RF) pulse consisting of two summed component pulses: an off-resonant pulse that induces a $B_1^{+}$ -dependent Bloch-Siegert frequency shift and a frequency-selective excitation pulse. The passband of the pulse can be tailored by adjusting the frequency content of the frequency-selective pulse, as in conventional $B_0$ gradient-localized excitation. Fine magnetization profile control is achieved by using the Shinnar-Le Roux algorithm to design the frequency-selective excitation pulse. Simulations analyzed the pulses' robustness to off-resonance, their suitability for multi-echo spin echo pulse sequences, and how their performance compares to that of rotating-frame selective excitation pulses. The pulses were evaluated experimentally on a 47.5 mT MRI scanner using an RF gradient transmit coil. Multiphoton resonances produced by the pulses were characterized and their distribution across $B_1^{+}$ predicted.

Results: With correction for varying $B_1^{+}$ across the desired profile, the proposed pulses produced selective excitation with the specified profile characteristics. The pulses were robust against off-resonance and RF amplifier distortion, and suitable for multi-echo pulse sequences. Experimental profiles closely matched simulated patterns.

Conclusion: The Bloch-Siegert shift can be used to perform $B_0$ -gradient-free selective excitation, enabling the excitation of slices or slabs in RF gradient-encoded MRI.

Keywords: Bloch-Siegert shift; RF pulse design; RF-encoded MRI; low-field MRI; multiphoton; selective RF excitation.

Figure 1

a) Construction of a BSSE RF pulse. The Bloch-Siegert shift producing pulse b_bs(t) (top left) and slice-selective pulse b_ex(t) (bottom left) are designed independently and summed into the full BSSE waveform b_total(t). b_bs(t) has Fermi AM (black) and adiabatic frequency sweeps towards and away from a constant frequency offset ω_off (orange). b_ex(t) has SLR-designed AM (black) and a constant frequency offset (orange). The amplitude of the b_bs(t) waveform is generally much larger than that of the b_ex(t) waveform; in |b_total(t)|, b_ex(t) is visible as a small ripple in the plateau of the Fermi waveform. b) Bloch-Siegert shift-localized slice selection, in which an off-resonant RF pulse produces an approximately quadratic variation in resonant frequencies across field strengths $B_1^{+}$. When paired with a frequency-selective excitation pulse, this results in the excitation of spins across a range $\Delta B_1^{+}$, which can be mapped to space using an amplitude gradient transmit coil.

Figure 2

a) SLR design algorithm to compensate for a sloped excitation profile across $B_1^{+}$. In the case of small-tip (‘st’) or 90° (‘ex’, ‘sat’) excitation, a pointwise scaling of the B_N(ω) profile is sufficient. For an inversion (‘inv’) or refocusing (‘se’) pulse, iterative refinement is required. b) Uncorrected and corrected 30°, PBC = 0.15 mT, PBW = 0.06 mT, T_exB = 8 excitation. c) Uncorrected and corrected 90° excitation. d) Uncorrected and corrected inversion profile after autodifferentiated gradient descent optimization of the pulse with respect to its magnetization profile, Iterative refinement corrected the highly distorted transition bands of the profile.

Figure 3

a) Variation in BSSE pulse duration with ω_off and PBC in $B_1^{+}$. Pulse duration increases with increasing ω_off and decreases with increasing $B_1^{+}$ PBC. The magnetization profiles of pulses designed at the three points of interest are plotted in (b). b) Magnetization profiles of BSSE pulses with PBC=0.14mT. Out-of band excitation can be large if ω_off is set too small: a pulse with ω_off = 2.5 kHz produces a substantial amount of out-of-band excitation, which is reduced to within design specifications when ω_off → 5.0 kHz. Further increasing ω_off to 10.0 kHz produced only marginal improvement.

Figure 4

a) Magnitude of a T = 3.7 ms BSSE inversion pulse. The pulse is colored red during the adiabatic frequency sweeps when b_ex(t) = 0, and blue during the constant portion of b_bs(t) when b_ex(t) ≠ 0. b) Motion of the net magnetization vector in the ω_off rotating frame for a stopband isochromat. Simulation timestep was 4 µs. At the end of the pulse, magnetization is essentially unperturbed. c) Motion of the net magnetization vector in the ω_off rotating frame for a passband isochromat. At the end of the pulse, magnetization is successfully inverted.

Figure 5

a) Flip angle attenuation factor versus ω_cent/ω_off. Data points are empirical correction factors found through simulation, with an exponential fit to the data shown as a continuous line. The red dot indicates the parameters of the pulse simulated in (b). b) Excited slice profile of a PBC =0.14 mT, PBW = 0.03 mT, 45°, ω_off =7.5 kHz pulse with and without the empirical FA correction. For this pulse, ω_cent/ω_off = 0.279, which the model predicts will result in a flip angle attenuation of 6.9% if uncorrected. Applying the correction improves the effective flip angle of the pulse, bringing it closer to the anticipated |M_xy|/M₀ = 0.7

Figure 6

a) Magnitudes of 90°, 180°, and 720° BSSE pulses with ω_off = 7.5 kHz (black) and ω_off = 15.0 kHz (red). b) The corresponding simulated magnetization profiles. Multiphoton resonances are visible at the locations in $B_1^{+}$ predicted by Equation 6. Increasing ω_off shifts resonances N ≥ 3 upward in $B_1^{+}$.

Figure 7

Simulations of BSSE and RFSE pulse off-resonance sensitivity. a) Simulation of the “base” 6.27ms BSSE and RFSE pulses with TB=4, PBC=0.4 mT, PBW=0.03 mT, FA=90°. ω_off was set to 16.37 kHz to match the RFSE pulse duration. b) Same as base pulse but with PBW set to 0.06 mT. ω_off was set to 9.48 kHz to match durations. c) Same as base but with TB set to 8. ω_off was set to 19.25 kHz to match durations. d) Same as base but with PBC set to 0.15. ω_off was set to 8.17 kHz to match durations. In all cases, the BSSE magnetization profiles show a bulk shift in the magnetization profile with increasing off-resonance. The red arrow in d) shows the location of an N = 3 multiphoton resonance. This multiphoton resonance also experiences a bulk shift downward in $B_1^{+}$ with increasing off-resonance. The RFSE profiles show no bulk shift, but have substantial unintended excitation at low $B_1^{+}$.

Figure 8

Simulation of RF amplifier droop. AM waveforms for RFSE (a) and BSSE (c) RF pulses are shown with −1.5dB of droop. In the case of the RFSE pulse, the magnetization profile (b) is severely degraded by RF amplifier distortion. However, the magnetization profile of the BSSE pulse (d) experiences only a slight shift upward in $B_1^{+}$, with minimal profile distortion.

Figure 9

BSSE Multi-echo CPMG pulse sequence. a) Pulse sequence diagram. A 90° excitation pulse was followed by a train of 180° pulses. To satisfy the CPMG phase conditions, RF pre- and re-winders were inserted before and after the 180° refocusing pulses. b) |β²| refocusing efficiency profile for the refocusing pulse. Refocusing was selective and nearly complete across the passband. The gradient descent-refined 180° pulse had a slightly improved profile, although the unrefined pulse also performs well given the narrow PBW. c) Signal timecourse in the passband and stopband. Regularly spaced echos of uniform amplitude were produced in the passband.

Figure 10

a) 47.5 mT permanent magnet system used for experimental results. A Faraday cage (red arrow) and pickup coil (blue arrow) are used to reduce EMI. b) variable-pitch T/R solenoid coil used in experiments. The tube phantom is placed inside in this image. c-f) middle slice of 3D GRE acquisition with varying BSSE excitation pulse. g) $B_1^{+}$ map corresponding to the same slice h) 1D simulated profiles for the pulses, and i) corresponding experimental 1D profiles. The 45° excitation (green) produces reduced signal intensity in relation to the 90° excitation (blue). The TB=1.5 excitation (red) produces a profile with a broader transition region. Designing the pulse with PBC shifted to 1.1 G (orange) produces the corresponding change in the magnetization profile.